NMR has been a common laboratory technique for over forty years and has become an important tool in formation evaluation. General background of NMR well logging can be found, for example, in commonly owned U.S. Pat. No. 5,023,551 to Kleinberg et al., incorporated herein by reference in its entirety.
NMR relies upon the fact that the nuclei of many chemical elements have angular momentum (“spin”) and a magnetic moment. In an externally applied static magnetic field, the spins of nuclei align themselves along the direction of the static field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field (e.g., an RF pulse) that tips the spins away from the static field direction. The angle through which the spins are tipped is given by θ=γB1tp/2, where γ is the gyromagnetic ratio, B1 is the linearly polarized oscillating field strength, and tp is the duration of the pulse. Tipping pulses of ninety and one hundred eighty degrees are most common.
After tipping, two things occur simultaneously. First, the spins precess around the direction of the static field at the Larmor frequency, given by ω0=γB0, where B0 is the strength of the static field and γ is the gyromagnetic ratio. For hydrogen nuclei, γ/2π=4258 Hz/Gauss, so, for example, in a static field of 235 Gauss, the hydrogen spins would precess at a frequency of 1 MHz. Second, the spins return to the equilibrium direction according to a decay time, T1, which is known as the spin-lattice relaxation time.
Also associated with the spin of molecular nuclei is a second relaxation time, T2, called the spin-spin relaxation time. At the end of a ninety-degree tipping pulse, all the spins are pointed in a common direction perpendicular, or transverse, to the static field, and they all precess at the Larmor frequency. However, due to small fluctuations in the static field induced by other spins or paramagnetic impurities, the spins precess at slightly different frequencies, and the transverse magnetization dephases with a time constant T2.
A standard technique for measuring T2, both in the laboratory and in well logging, uses an RF pulse sequence known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence. As is well known, after a wait time that precedes each pulse sequence, a ninety degree pulse causes the spins to start precessing. Then, a one hundred eighty degree pulse is applied that keeps the spins in the measurement plane, but causes the spins, which are dephasing in the transverse plane, to reverse direction and to refocus. By repeatedly reversing the spins using a series of one hundred eighty degree pulses, a series of “spin echoes” appear. The train of echoes is measured and processed to determine the irreversible dephasing, T2.
In a uniform static magnetic field, each spin will experience the same magnetic field strength regardless of its position within the static field, and diffusion will not contribute to the observed relaxation rate, as defined in equation (1) below.                               1                      T            2                          =                              1                          T                              2                ,                bulk                                              +                      1                          T                              2                ,                diffusion                                                                        (        1        )            
In a magnetic field gradient, however, each spin will experience different magnetic field strengths as it diffuses through the static field. The Larmor frequencies of the diffusing spins become time dependent, and the series of one hundred eighty degree pulses cannot refocus the spins completely, leading to an additional decay signal. This additional decay signal is proportional to the diffusion coefficient, D, of the fluid and to the square of the gradient strength, g, and the square of the echo spacing, tE, i.e.,                               1                      T                          2              ,              diffusion                                      =                              1            12                    ⁢                      γ            2                    ⁢                      g            2                    ⁢          D          ⁢                                           ⁢                                    t              E              2                        .                                              (        2        )            
Because the diffusion coefficient provides an indication of fluid type, measurement of the diffusion effects on the distribution of decay times ƒ(T2) can be used as the basis for determining the characteristics of formation fluids.
Certain NMR measurements of diffusion involve changing the echo spacing, tE, in a standard CPMG sequence, and thus, the amount of diffusion the spins undergo between echoes, and then comparing the measured relaxations. FIGS. 1A and 1B generally illustrate this approach. FIG. 1A shows two CPMG sequences with different echo spacings, t1 and t2, where t2 is longer than t1. As the echo spacing increases, the spins diffuse further between echoes, and the measured relaxation times will decrease depending on the diffusion coefficient of the fluid, as given in Equation 2 above. FIG. 1B shows the relaxation distributions, ƒ(T2), for an oil and water determined from the two sets of echoes acquired from the two CPMG sequences illustrated in FIG. 1A. As seen in FIG. 1B, the relaxation distribution with the longer echo spacing, t2, is shifted to lower relaxation times, T2, relative to the relaxation distribution with the shorter echo spacing, t1. The size of the shift is proportional to the size of the diffusion coefficient, as indicated by arrows 1 and 2. The shift of ƒ(T2) for a fluid with a small diffusion coefficient 1, such as heavy oil, is smaller than the shift for a fluid with a larger diffusion coefficient 2, such as water or natural gas.
While such NMR diffusion measurements can be useful, they suffer from a number of drawbacks. For example, for a given acquisition time, the two CPMG sequences will not have the same number of echoes. The CPMG sequence with longer echo spacing will have a fewer number of echoes available and will suffer from lower signal to noise and lower data quality in general. In addition, relaxation distributions for different fluids often overlap, at least partially, making it difficult to identify shifts of individual relaxation times. In cases where the diffusion coefficients for different fluids are small, the shifts may be difficult to distinguish. Finally, these methods cannot separate out the contributions due to diffusion effects from bulk relaxation contributions in the observed relaxation distributions.
Accordingly, one object of the present invention is to provide a method and apparatus for determining characteristics of fluid using NMR techniques wherein effects from relaxation and diffusion may be measured separately.